Proving that the matrix is invertible given the eigenvalues?

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Homework Statement


Given an unknown matrix with eigenvalues 1,2,3, prove that it is invertible?

The Attempt at a Solution


If the det = 0, then there exists an eigenvalue = 0. Since none of the eigenvalues are 0, then the det ≠ 0 and thus the matrix is invertible. Is this a valid proof?
 

Answers and Replies

  • #2
HallsofIvy
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Yes, it is.
 

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